A341275 a(n) = 2^(n*(n-1)/2)*Product_{j=0..n-1} (4*j+2)!/(n+2*j+1)!.

1, 4, 60, 3328, 678912, 508035072, 1392439459840, 13965623033856000, 512247880383410995200, 68683284942451522425323520, 33654191472236763924706696888320, 60248257274480672292932706180054122496, 393994689318303735728047162574735199856230400

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..60

Philippe Di Francesco, Twenty Vertex model and domino tilings of the Aztec triangle, arXiv:2102.02920 [math.CO], 2021.

Frederick Huang, The 20 Vertex Model and Related Domino Tilings, Ph. D. Dissertation, UC Berkeley, 2023. See p. 1.

Formula

a(n) ~ exp(1/48) * Pi^(1/4) * 2^(9*n^2/2 + n/2 + 1/3) / (sqrt(Gamma(1/4)) * A^(1/4) * n^(7/48) * 3^(9*n^2/4 + 3*n/4 - 1/24)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 08 2021

Mathematica

Table[2^(n*(n-1)/2) * Product[(4*j + 2)!/(n + 2*j + 1)!, {j, 0, n-1}], {n, 1, 15}] (* Vaclav Kotesovec, Feb 08 2021 *)

Prog

(PARI) a(n) = 2^(n*(n-1)/2)*prod(j=0, n-1, (4*j+2)!/(n+2*j+1)!);

Crossrefs

Sequence in context: A012567 A132627 A229771 * A338550 A340937 A136385

Adjacent sequences: A341272 A341273 A341274 * A341276 A341277 A341278

Keyword

nonn

Author

Michel Marcus, Feb 08 2021

Status

approved